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on Game Theory |
| By: | Andreas Park; Lones Smith |
| Abstract: | There are two varieties of timing games in economics: Having more predecessors helps in a war of attrition and hurts in a pre-emption game. This paper introduces and explores a spanning class with rank-order payoffs} that subsumes both as special cases. We assume a continuous time setting with unobserved actions and complete information, and explore how equilibria of these games capture many economic and social timing phenomena --- shifting between phases of slow and explosive (positive probability) stopping.<p> Inspired by auction theory, we first show how the symmetric Nash equilibria are each equivalent to a different "potential function". This device straightforwardly yields existence and characterization results. The Descartes Rule of Signs, e.g., bounds the number phase transitions. We describe how adjacent timing game phases interact: War of attrition phases are not played out as long as they would be in isolation, but instead are cut short by pre-emptive atoms. We bound the number of equilibria, and compute the payoff and duration of each equilibrium. |
| Keywords: | Games of Timing, War of Attrition, Preemption Game. |
| JEL: | C73 D81 |
| Date: | 2008–04–29 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-317&r=gth |
| By: | Mallesh Pai; Rakesh Vohra |
| Abstract: | We consider a dynamic auction problem motivated by the traditional single-leg, multi-period revenue management problem. A seller with C units to sell faces potential buyers with unit demand who arrive and depart over the course of T time periods. The time at which a buyer arrives, her value for a unit as well as the time by which she must make the purchase are private information. In this environment, we derive the revenue maximizing Bayesian incentive compatible selling mechanism. |
| Keywords: | dynamic mechanism design, optimal auctions, virtual valuation, revelation principle |
| JEL: | D44 C72 C73 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1461&r=gth |
| By: | J. Abdou (University Paris 1); Hans Keiding (Department of Economics, University of Copenhagen) |
| Abstract: | We introduce a description of the power structure which is inherent in a strategic game form using the concept of an interaction sheaf. The latter assigns to each open set of outcomes a set of interaction arrays, specifying the changes that coalitions can make if outcome belongs to this open set. The interaction sheaf generalizes the notion of effectivity functions which has been widely used in implementation theory, taking into consideration that changes in outcome may be sustained not only by single coalitions but possibly by several coalitions, depending on the underlying strategy choices. Also, it with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding (2003). |
| Keywords: | Nash equilibrium; strong equilibrium; solvability; effectivity; acyclicity |
| JEL: | C70 D71 |
| Date: | 2008–04 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:0812&r=gth |
| By: | Dan Kovenock; Brian Roberson |
| Abstract: | This paper examines a multi-player and multi-front Colonel Blotto game in which one player, A, simultaneously competes in two disjoint Colonel Blotto games, against two separate opponents, 1 and 2. Prior to competing in the games, players 1 and 2 have the opportunity to form an alliance to share their endowments of a one-dimensional resource (e.g., troops, military hardware, money). This paper examines “non-cooperative” alliances in which only individually rational ex ante transfers of the resource are allowed. Once these transfers take place, each alliance member maximizes his payoff in his respective Colonel Blotto game, given his resource constraint and player A’s allocation of its endowment across the two games. No ex post transfers are enforceable. Remarkably, there are several ranges of parameters in which endogenous unilateral transfers take place within the alliance. That is, one player gives away resources to his ally, who happily accepts the gift. Unilateral transfers arise because they lead to a strategic shift in the common opponent’s force allocation away from the set of battlefields of the player making the transfer, towards the set of battlefields of the player receiving the transfer. Our result demonstrates that there exist unilateral transfers for which the combination of direct and strategic effects benefits both allies. This stands in stark contrast to the previous literature on alliances (see Sandler and Hartley, 2001), which relies on the assumption of pure or impure public goods. |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1207&r=gth |
| By: | Lugovskyy, Volodymyr; Puzzello, Daniela; Tucker, Steven |
| Abstract: | Pervasive overbidding represents a well-documented feature of all-pay auctions. Aggregate bids exceed Nash predictions in laboratory experiments, and individuals often submit bids that guarantee negative profits. This paper examines three factors that may reduce pervasive overbidding: (a) repetition (experience), (b) reputation (strangers vs. partners) and (c) active participation. We find that aggregate over-dissipation diminishes but is not eliminated with repetition, and that repetition, in conjunction with active participation generates bids consistent with the static Nash predictions. |
| JEL: | C9 D72 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8604&r=gth |
| By: | Ludovic Renou |
| Abstract: | This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004)). |
| Keywords: | Minimax regret, rationality, conjectures, price dispersion, auction |
| JEL: | C7 |
| Date: | 2008–04 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1087&r=gth |
| By: | Gunnthorsdottir, Anna; Vragov, Roumen; seifert, Stefan; McCabe, Kevin |
| Abstract: | According to theory a pure meritocracy is efficient because individual members are competitively rewarded according to their individual contributions to society. However, purely individually based meritocracies seldom occur. We introduce a new model of social production called “team-based meritocracy” (TBM) in which individual members are rewarded based on their team membership. We demonstrate that as long as such team membership is both mobile and competitively based on contributions, individuals are able to tacitly coordinate a complex and counterintuitive asymmetric equilibrium that is close to Pareto-optimal, possibly indicating that such a group-based meritocracy could be a social structure to which humans respond with particular ease. Our findings are relevant to many contemporary societies in which rewards are at least in part determined via membership in organizations such as for example firms, and organizational membership is increasingly determined by contribution rather than privilege. |
| Keywords: | social stratification; meritocracies; mechanism design; non-cooperative games; experiment; team production. |
| JEL: | D20 C72 |
| Date: | 2008–01–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8627&r=gth |
| By: | Lahiri, Somdeb |
| Abstract: | In this paper we provide sufficient conditions for the existence stable matchings for three-sided systems. |
| JEL: | C78 |
| Date: | 2008–05–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8660&r=gth |
| By: | Molzon, Robert; Puzzello, Daniela |
| Abstract: | Random matching is often used in economic models as a means of introducing uncertainty in sequential decision problems. We show that random matching schemes that satisfy standard conditions on proportionality are not unique. Two examples show that in a simple growth model, radically di¤erent optimal behavior can result from distinct matching schemes satisfying identical proportionality conditions. That is, non-uniqueness has interesting economic implications since it a¤ects the reward and the transi- tion structures. We propose information entropy as a natural method for selecting unique matching structures for these models. Next, we give conditions on the reward and transition structures of sequential decision models under which the models are not a¤ected by non-uniqueness of the matching scheme. |
| JEL: | D83 C73 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8603&r=gth |